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Topic: CANTORS PROOF DEMO the Reals are UN-COUNTABLE
Replies: 2   Last Post: Jan 22, 2013 9:00 PM

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Posts: 821
Registered: 9/1/10
Re: AND THIS PROOF CONCLUSION IS TRUE?
Posted: Jan 22, 2013 9:00 PM
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On Jan 10, 5:34 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
> > A SUBLIST OF REALS IN  [BASE 4]
>
> > R1  0.0000...
> > R2  0.3333...
> > R3  0.3210...
> > ...

>
> > DIAGONAL = 0.031...
>
> > DEFINE
> > AD(d) = 2 IFF DIAGONAL(d) < 2
> > AD(d) = 1 IFF DIAGONAL(d) > 1

>
> > AD=0.212...   is MISSING FROM THE LIST
>
> > PROOF
> > DIGIT 1 (2)   IS DIFFERENT TO LIST[1,1]   (0)
> > DIGIT 2 (1)   IS DIFFERENT TO LIST[2,2]   (3)
> > DIGIT 3 (2)   IS DIFFERENT TO LIST[3,3]   (1)
> > AND SO ON

>
> > So AD is DIFFERENT to EVERY ROW
> > since This Holds For Any Arbitrary List Of Reals
> > there is a missing Real for any List Of Reals
> > therefore Reals are Un-Countable!

>
> > Herc

YES



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